MinT - Best Known (144, 144+47, s)-Nets in Base 4

Best Known (144, 144+47, s)-Nets in Base 4

(144, 144+47, 1028)-Net over F₄ — Constructive and digital

Digital (144, 191, 1028)-net over F₄, using

1 times m-reduction [i] based on digital (144, 192, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 48, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(144, 144+47, 1919)-Net over F₄ — Digital

Digital (144, 191, 1919)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+47, 295696)-Net in Base 4 — Upper bound on s

There is no (144, 191, 295697)-net in base 4, because

1 times m-reduction [i] would yield (144, 190, 295697)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 462657 901294 407996 321828 005832 862342 851595 825170 438351 044648 427490 961121 994322 824651 366521 668062 975494 447746 962688 > 4¹⁹⁰ [i]